Predicting a day's data
Just for clarification: your description (1 sample per minute) does not match the example data (far fewer data points which is understandable, but also two data points in one minute which contradicts the initial assertion.) If your actual measurements are like that you should first work on the sampling process to get reliable data.

For creating predictions, you need to have a reasonable model of the observed process. If you're measuring environmental temperatures, you will basically have three causes of variation:


A day/night cycle
A seasonal (summer/winter) cycle
Local weather fluctuation


From only one day of samples, the only thing you can reasonably predict is that the next day will look mostly the same. If you collect more data over a year, you will be able to extract a seasonal cycle and estimate the deviations caused by local weather. "You" means either you as a researcher or any machine learning system that you program. Without sufficient historical data it is impossible to make good predictions (and even with sufficient data it's hard.)